## 4.2.5 Variability of CUR size distributions

Up to now, we have only explored the average CUR size distributions of the toy model and nothing has been said about their variability for different realizations. Although this variability should vanish for infinitely long sequences (CUR size distributions are self-averaging in the thermodynamic limit) there are large fluctuations for finite length molecules. This variability can be determined from the same simulations of the toy model that have been used in the previous sections. Now, for all the realizations we do not only calculate the average CUR size distribution but the standard deviation of the distribution at each value of . So if we have a collection of distributions obtained from realizations, =1,,, we can compute the average distribution and the standard deviation of the distribution according to (see Fig. 4.13),

 (4.11)

JM Huguet 2014-02-12